Assuming there are 11,000 births per day, the average timespan between twin births is 17 minutes, and 1/30 births are twin births, what are the chances that a couple will have two twins born in a different years?

This assumes that births are evenly distributed. In fact there is a significant drop in births on Jan 1, Jul 4, and Dec 25. People tend to avoid holidays when it comes to giving birth. If there's one particular moment that people tend to avoid, it's probably going to be midnight on the new year.

EDIT: But apparently 3 out of ~4 million births in 2012 fall into this category, putting the odds (3 in 4 million), about 1.5x OP's estimate.